Question

[Phạm Hoàng Phú]

Tính:1 1/3 x 1 1/8 x 1 1/15 x 1 1/24 x...x 1 1/99

Answer 1

[Nguyễn Thị Thương Hoài]

A =   1\(\dfrac{1}{3}\) x 1\(\dfrac{1}{8}\) x 1\(\dfrac{1}{15}\) x 1\(\dfrac{1}{24}\) x ... x 1\(\dfrac{1}{99}\)

A =   \(\dfrac{4}{3}\) x \(\dfrac{9}{8}\) x \(\dfrac{16}{15}\) x \(\dfrac{25}{24}\) x ... x \(\dfrac{100}{99}\)

A =   \(\dfrac{2\times2}{1\times3}\) x \(\dfrac{3\times3}{2\times4}\) x \(\dfrac{4\times4}{3\times5}\) x \(\dfrac{5\times5}{4\times6}\) x ... x \(\dfrac{10\times10}{9\times11}\)

A =    \(\dfrac{\left(2\times3\times...\times9\times10\right)\times\left(2\times3\times4\times...\times10\right)}{\left(1\times2\times3\times..\times9\right)\times\left(3\times4\times..\times10\times11\right)}\)

A =    (\(\dfrac{2\times3\times..\times9}{2\times3\times..\times9}\times\dfrac{10}{1}\)) x (\(\dfrac{3\times4\times...\times9\times10}{3\times4\times...\times9\times10}\) \(\times\)\(\dfrac{2}{11}\) )

A =    \(\dfrac{10}{1}\) \(\times\) \(\dfrac{2}{11}\) 

A =    \(\dfrac{20}{11}\)

Answer 2

[Nguyễn Lê Phước Thịnh]

\(1\dfrac{1}{3}\cdot1\dfrac{1}{8}\cdot...\cdot1\dfrac{1}{99}\)

\(=\dfrac{4}{3}\cdot\dfrac{9}{8}\cdot...\cdot\dfrac{100}{99}\)

\(=\dfrac{2\cdot3\cdot...\cdot10}{1\cdot2\cdot...\cdot9}\cdot\dfrac{2\cdot3\cdot...\cdot10}{3\cdot4\cdot...\cdot11}\)

\(=\dfrac{10}{1}\cdot\dfrac{2}{11}=\dfrac{20}{11}\)